Fuzzy Metric Space and Its Topological Properties

Authors

  • Masriani Masriani Department of Mathematics, Universitas Mataram
  • Qurratul Aini Department of Mathematics, Universitas Mataram
  • Syamsul Bahri Department of Mathematics, Universitas Mataram

DOI:

https://doi.org/10.29303/emj.v4i2.95

Keywords:

fuzzy sets, fuzzy metric space, fuzzy metric space topological charaters

Abstract

The fuzzy set theory is mathematics that applies fuzziness characteristics, so that gives the truth value at interval [0,1]. It is different from the crisp set that gives a truth value of 0 if it is not a member and 1 if it is a member. The theory of fuzzy sets has been developed continuously by scientists. One of the developments of the fuzzy set is the fuzzy metric space which the definition was introduced by George and Veeramani. Based on the analysis results, it is found that every metric space X if and only if X is fuzzy metric space. As a result, the topological properties of the metric space still apply to the fuzzy metric space

References

Aphane,M. (2009). On Some Results of Analysis in Metric Spaces and Fuzzy Metric Spaces. Pretoria: University of South Africa,

David, S. D., & Richard, M. F. (2004). Abstract Algebra 3 Edition. New York: Prentice-Hall. Inc.

George, A., & Veeramani, P. (1994). On Some Results In Fuzzy Metric Spaces. Fuzzy Sets and System, 64, 395-399.

Gregori, V., Morillas , S., & Sapena , A. (2009). On Convergence In Fuzzy Metric Spaces. Topology and Its Aplications, 156, 3002-3006.

Korner, T. W. (2014). Metric and Topological Spaces. 1-109.

Kramosil, I., & Michálek, J. (1975). Fuzzy Metrics and Statistical Metric Spaces. Kybernetika, 11(5), 336-334. .

Nasution, H. (2012). Implementasi Logika Fuzzy pada Sistem Kecerdasan Buatan. ELKHA, 4, 4-8.

Roopkumar, R., & Vembu, R. (1991). Some Remarks On Metrics Induced By a Fuzzy Metric. Mathematics Subject Classification, 1.

Ruseffendi, ET. . Pengajaran Matematika Modern Untuk Orangtua, Murid, Guru dan SPG. Bandung: Tarsito.

Wang, L. X. (1997). A Course In Fuzzy System And Control. United States: Prentice-Hall International. Inc.

Zadeh, L. A. (1965). Fuzzy Sets. Information and Control, 8, 338-353.

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Published

2022-01-06

How to Cite

Masriani, M., Aini, Q., & Bahri, S. (2022). Fuzzy Metric Space and Its Topological Properties. EIGEN MATHEMATICS JOURNAL, 4(2), 74–79. https://doi.org/10.29303/emj.v4i2.95

Issue

Vol. 4 No. 2 Desember 2021

Section

Articles

License

All articles published in the Eigen Mathematics Journal will be available for free reading and downloading. The license applied to this journal is Creative Commons Attribution-Non-Commercial-Share Alike (CC BY-NC-SA).

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